Intersecting D-brane Models

Abstract

This thesis is devoted to the study of a class of constructions based on Superstring Theory, baptized in the literature as Intersecting Brane Worlds. In particular we explore several issues regarding the proposal of Intersecting Brane Worlds as string-based models yielding semi-realistic low-energy physics. We find that they provide an interesting framework where, for instance, just the Standard Model chiral content and gauge group can be obtained. Although many of the results presented in this work are valid for more general constructions, we center on configurations of D-branes intersecting at angles. We construct several classes of such compactifications which may yield realistic D=4 physics. We build several explicit examples giving the Standard Model chiral spectrum, and then proceed to analyze some of the related phenomenology. We pay special attention to features such as the structure of U(1) global symmetries, the absence of open-string tachyons, the appearance of light extra matter and the possibility of lowering the string scale in such scenarios. Finally, we investigate the relationship between low-energy field theory quantities, such as FI-parameters and Yukawa couplings, with the geometrical objects underlying the string construction. We find that their description is closely related to calibration theory and to the construction of Fukaya's category.

Figures (32)

• Figure 1: Particle, open string and membrane propagation through spacetime, sweeping a one, two and three-dimensional trajectory on $M_{10}$, respectively. Figure taken from Duff:2001jp.
• Figure 2: $T^2/{\bf Z}_3$ orbifold. Both axis of the torus are identified under the action of the ${\bf Z}_3$ generator, which is a $2\pi/3$ rotation over the origin $O$. The vector $V$ is parallel transported to $V'$, which makes an angle of $2\pi/3$ with the image of $V$ under the orbifold action.
• Figure 3: Situation of string theory after the second superstring revolution. The previously disconnected five superstring theories are nothing but specific (limiting) points in the parameter space of a more fundamental theory: M-theory.
• Figure 4: Two D5-branes intersecting at angles in $M_{10}$. Both D-branes are parallel in the $2^{nd}$ complex plane, having a separation $Y^3$ in such plane and vanishing intersection. The angles are to be measured as indicated in the figure, going from brane $a$ to $b$ in the $ab$ sector, with the counterclockwise sense yielding a positive angle.
• Figure 5: D-brane wrapped on the minimum length 1-cycle on the homology class $[(n,m)] = [(3,2)] \in H_1(T^2,{\bf Z})$. Fixed this homology class, the angle $\theta$ between the D-brane and the $x_1$ axis will depend on the torus complex structure $\tau^\prime$.